Question

which circle has a radius that measures 10 units?

Explanation:

Step1: Recall the definition of radius and diameter

The radius \(r\) of a circle is the distance from the center of the circle to any point on the circle. The diameter \(d\) of a circle is the distance across the circle through its center, and the relationship between the radius and the diameter is \(d = 2r\) or \(r=\frac{d}{2}\).

Step2: Analyze each option

• Option with center \(D\): The given length is a radius (since it is from the center to a point on the circle). If the length is \(10\), then \(r = 10\) units.
• Option with center \(F\): The given length is a diameter (\(d=20\)). Using the formula \(r=\frac{d}{2}\), we get \(r=\frac{20}{2}=10\). But this is a diameter - labeled as \(20\), not a radius.
• Option with center \(G\): The given length is a diameter (\(d = 10\)). Using the formula \(r=\frac{d}{2}\), we get \(r=\frac{10}{2} = 5\) units.
• Option with center \(H\): The given length is a chord (not passing through the center), not a radius.

Answer:

The circle with center \(D\) has a radius that measures \(10\) units.